F.4 Maths Sine Formula

👨🏻‍🏫 學術台數學

[匿名]

2011-04-08 4:29 am

1. In the figure, B=50度 and AB:AC=3:4. Find C.

2.In the figure, DB us tge angle bisector of angle ABC in triangle ABC. Show that sinA/DC = sinC/DA.

更新1:

No. 2 should be "In the figure, DB is the angle bisector of angle ABC in triangle ABC. ......." Sorry!

回答 (1)

用戶2053

2011-04-08 4:48 am

✔ 最佳答案

1)sinC : sinB = AB : ACsinC : sin50° = 3 : 4sinC = (3/4)sin50° C = 35.067° or C = 144.933° 2)Consider △ADB ,
sinA / BD = sin(B/2) / DA ....(1)Consider △DCB ,
sinC / BD = sin(B/2) / DC ....(2)(1) / (2) :(sinA / BD) / (sinC / BD) = [sin(B/2) / DA ] / [sin(B/2) / DC]sinA / sinC = DC / DAsinA / DC = sinC / DA

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